1. Field of the Invention
The invention relates generally to techniques for formation resistivity logging using induction tools. More particularly, the invention relates to methods and systems for correcting borehole effects in resistivity measurements obtained with induction tools that include transverse or triaxial arrays.
2. Background Art
Induction tools are used in the oil and gas industry to determine the resistivity of earth formations surrounding a borehole. Induction tools work by using a transmitting coil (transmitter) to set up an alternating magnetic field in the earth formations. This alternating magnetic field induces eddy currents in the formations. One or more receiving coils (receivers), disposed at a distance from the transmitter, are used to detect the current flowing in the earth formation. The magnitudes of the received signals are proportional to the formation conductivity. Therefore, formation conductivities may be derived from the received signals.
However, heterogeneities in the formation complicate the derivation of formation conductivity from the received signals. The most prevalent complication that affects the derivation of formation conductivity from the received signals arises from the presence of conductive fluids in the borehole surrounding the induction instrument. This is referred to generally as the borehole effects. Often, the fluids in the borehole (drilling mud) are made very saline, thus conductive, as part of the drilling practice. The conductive drilling muds can contribute a significant proportion of the received signals and, therefore, should be carefully removed.
Recently, transverse induction instruments have been developed for investigating the resistivities of formations with anisotropy, dipping planes, faults, or fractures. These transverse induction instruments have transmitting and receiving coils arranged such that the magnetic moments of the transmitter and/or receiver coils are perpendicular to the axis of the borehole. It is well known that the borehole effects of transverse coil arrangements are very large when the instrument is moved eccentrically in the borehole in the direction perpendicular to the coil magnetic moments. See e.g., Moran and Gianzero, “Effects of Formation Anisotropy on Resistivity Logging Measurements,” Geophysics, 44, 1266-1286 (1979).
The cause of the eccentricity effect of transverse coils is disclosed in U.S. Pat. No. 6,573,722, issued to Rosthal et al. This patent teaches a method for mitigating the eccentric borehole effects of an induction tool. Specifically, this patent discloses tool designs in which an induction tool includes a conductive member in its insulating sleeve or the induction tool includes a conductive tool body. These conductive parts greatly reduce the borehole effects of such an instrument, but does not remove all of the effects. Further correction would be necessary to completely remove the borehole effects of a transverse induction instrument.
U.S. Pat. No. 5,041,975, issued to Minerbo et al. discloses a method for correcting borehole effects of array induction instruments. This method uses the data from the 4 shortest arrays of an array induction tool, along with approximate measurements of the hole size and the borehole fluid conductivity, to solve for 2 parameters in a 4-parameter borehole-formation model. The model consists of a borehole having a radius r drilled in a homogeneous formation of conductivity □f. The borehole fluid has a conductivity □m, and the induction tool is located at a distance (standoff) s from the borehole wall. A fast forward model consists of a large table built from a number of cases over appropriate ranges of the 4 parameters. An inversion process minimizes the penalty function E, which is the sum of the squares of a weighted difference between the measured response and predicted response, as shown in Equation (1):
                              E          ⁡                      (                                          σ                _                            f                        )                          =                              ∑                          j              =              1                        4                    ⁢                                                                                                                                  σ                      meas                      j                                        -                                                                  σ                        model                        j                                            ⁡                                              (                                                                              σ                            m                                                    ,                                                                                    σ                              f                                                        _                                                    ,                          r                          ,                          s                                                )                                                                                                              2                                            ɛ                j                                      .                                              (        1        )            
In this equation Equationσmeasj is the modeled conductivity from the j-th array with the given parameters □m, □f, r, and s. When E is minimized, the associated parameters □m, □f, r, and s are used to compute the borehole correction for all the arrays.
While effective methods are available for correcting borehole effects for axial arrays, transverse array instruments present special problems. The sensitivity of induction arrays with moments perpendicular to the axis of the borehole to eccentricity is very different depending on whether the eccentricity is in the direction of the magnetic moment or perpendicular to the magnetic moment. U.S. Pat. No. 6,556,015 issued to Omeragic et al. describes methods of reducing the effect of the borehole on induction measurements with transverse coils through mechanical or electromagnetic rotation of the tool about its axis. However, there still exists a need for better methods for borehole effect corrections that can be used with transverse array instruments.